A small stone of mass 50 g and volume 10 cm3 held under water is allowed to fall in it. The acceleration of stone in water is (Take g = 10 m/s2, ρw = 1000 kg/m3)2 m/s24 m/s26 m/s28 m/s2

The problem is asking for the acceleration of the stone in water. To solve this, we need to understand that the stone is subjected to two forces: the gravitational force (weight of the stone) and the buoyant force (upthrust due to water).

1. First, calculate the weight of the stone. The weight (W) is given by the formula W = m*g, where m is the mass and g is the acceleration due to gravity. Here, m = 50 g = 0.05 kg (since 1 kg = 1000 g) and g = 10 m/s². So, W = 0.05 kg * 10 m/s² = 0.5 N.

2. Next, calculate the buoyant force. The buoyant force (B) is given by the formula B = Vρwg, where V is the volume of the stone, ρw is the density of water, and g is the acceleration due to gravity. Here, V = 10 cm³ = 10^-5 m³ (since 1 m³ = 10^6 cm³), ρw = 1000 kg/m³, and g = 10 m/s². So, B = 10^-5 m³ * 1000 kg/m³ * 10 m/s² = 0.1 N.

3. The net force acting on the stone is the difference between the weight and the buoyant force (F = W - B). So, F = 0.5 N - 0.1 N = 0.4 N.

4. Finally, use Newton's second law of motion (F = m*a) to find the acceleration of the stone (a). Here, F = 0.4 N and m = 0.05 kg. So, a = F/m = 0.4 N / 0.05 kg = 8 m/s².

So, the acceleration of the stone in water is 8 m/s².